Diagnosing Errors in the Structure of Rossby Waves on the Extratropical Tropopause in Medium-Range Operational Weather Forecasts

Rossby waves propagating along the extratropical tropopause have a dominant impact on weather at the surface in midlatitudes via baroclinic instability. While forecasts of waves by numerical weather prediction systems are limited by intrinsic unpredictability due to initial condition sensitivity, the statistical properties of these features should not contain biases if the models are optimally designed. In this study, statistical properties of upper level waves in forecasts are evaluated for the seasons 2008-2012. Wavelet transforms are used to analyze Rossby wave amplitude as a function of both wavelength and longitude. The wavelet transforms are applied to both analysis and forecast potential vorticity. The difference between the two reveals model error. This process is done for three operational centers: ECMWF, UKMET, and NCEP, over 5 winter seasons. A comparison is made of 5 dependencies: forecast center, interseasonal variation, longitude, lead time, and wavelength. Additionally, a wave breaking diagnostic is developed as a supplemental tool for determining wave structure errors in operational models. Breaking frequency determines how many points of longitude in the wave pattern on average per day were breaking. The analysis reveals: 1) On average, Rossby wave amplitude is under forecast in all 5 dependencies, statistically significant at the 95% confidence level, 2) The largest errors are found in regions of climatologically higher wave activity, 3) errors in ECMWF are smaller and accumulate more steadily than UKMET and NCEP, which demonstrate large error very early in forecasts, 4) The errors represent biases in the model, not a regression to the mean, and 5) There are large errors in the wave breaking frequency for all forecast centers. The results imply an inherent issue in operational models with forecasting wave amplitude. How the errors vary across the 5 dependencies and how the work may be expanded for further study are discussed.